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Bipartitional polynomials and their applications in combinatorics and statistics

1981
*
Discrete Mathematics
*

Recurrence relations, generating functions

doi:10.1016/0012-365x(81)90024-8
fatcat:viu6mybgnbc3nkqu2xge7v4cse
*and*some basic properties or these*polynomials*are given.*Applications**in**Combinatorics**and**Statistics*are briefiy indicated.. ...*Bipartitional**polynomials*are multivariable*polynomials*Y ,",*=Ynln(CYOI~CYlorCY,I~..-rCYlnn)r Ck'Ck, defined by a sum over ail partitions of the bpartite number (mn). ... Riordan [6, 7] called Bell*polynomials*the partition*polynomials*associated with the derivatives of a composite function; he discussed several*applications*of these*polynomials**in**Combinatorics*,*Statistics*...##
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Page 1390 of Mathematical Reviews Vol. , Issue 82d
[page]

1982
*
Mathematical Reviews
*

A. 82d:05010

*Bipartitional**polynomials**and**their**applications**in**combinatorics**and**statistics*. Discrete Math. 34 (1981), no. 1, 81-84. ... Recurrence relations, generalizing functions*and*some basic properties of these 82d:05009 1390*polynomials*are given.*Applications**in**combinatorics**and**statistics*are briefly indicated.” ...##
###
Page 6447 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

He remarks that rational series are probably not well known

*in**combinatorics*, although*their*one-variable version (linear recursive sequences) is certainly well known. ... Some new enumeration results for semiregular*bipartite*graphs are included,*and*the related cat- egory of the quasi-semiregular*bipartite*graphs is recognized. ...##
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Page 820 of Mathematical Reviews Vol. , Issue 2002B
[page]

2002
*
Mathematical Reviews
*

(English summary) Special issue on design

*combinatorics*:*in*honor of S. S. Shrikhande. J.*Statist*. Plann. Inference 95 (2001), no. 1-2, 197-208. ... Concentration of multivariate*polynomials**and*its*applications*. (English summary) Combinatorica 20 (2000), no. 3, 417-434. Let f = f(x),... ...##
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Page 1553 of Mathematical Reviews Vol. , Issue 2002C
[page]

2002
*
Mathematical Reviews
*

[Zhu, Lie'] (PRC-SOO; Suzhou)
V (m, ¢)

*and*its variants. (English summary) Special issue on design*combinatorics*:*in*honor of S.S. Shrikhande. J.*Statist*. Plann. ... The algorithm runs*in*time*polynomial**in*the size of V’*and*V°. This algorithm can be used to obtain a*polynomial*time algorithm for finding an unbalanced hole*in*a graph that contains one. ...##
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Discrete mathematics: methods and challenges
[article]

2002
*
arXiv
*
pre-print

*Combinatorics*is a fundamental mathematical discipline as well as an essential component of many mathematical areas,

*and*its study has experienced an impressive growth

*in*recent years. ... This is a survey of two of the main general techniques that played a crucial role

*in*the development of modern

*combinatorics*; algebraic methods

*and*probabilistic methods. ... These include

*applications*

*in*Information Theory

*and*Electrical Engineering,

*in*

*Statistical*Physics,

*in*Chemistry

*and*Molecular Biology,

*and*, of course,

*in*Computer Science. ...

##
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Page 7177 of Mathematical Reviews Vol. , Issue 95m
[page]

1995
*
Mathematical Reviews
*

These combinatorial problems have

*their*origins*in**statistical*mechanics.” ... (English summary)*Combinatorics*, graph theory, algorithms*and**applications*( Beijing, 1993), 17-20, World Sci. Publishing, River Edge, NJ, 1994. ...##
###
Page 4539 of Mathematical Reviews Vol. , Issue 91H
[page]

1991
*
Mathematical Reviews
*

(H-AOS-C)

*Polynomial*algorithms for finding cycles*and*paths*in**bipartite*tournaments. SIAM J. Discrete Math. 3 (1990), no. 4, 537-543. ... This paper presents algorithms for determining the existence of specific paths*and*cycles*in*a*bipartite*tournament (a complete directed*bipartite*graph). ...##
###
Page 918 of Mathematical Reviews Vol. , Issue 83c
[page]

1983
*
Mathematical Reviews
*

Combinatorial mathematics, optimal designs

*and**their**applications*(Proc. Sympos. Combin. Math.*and*Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978). Ann. ... . **Combinatorics**and*graph theory. 83c:05002 Proceedings of the Second Symposium held at the Indian*Statistical*© Institute, Calcutta, February 25-29, 1980. Edited by Siddani Bhaskara Rao. ...##
###
Page 4954 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

Using the

*combinatorics*of biwords (words over biletters) it is shown here how four such transformations that have occurred*in*earlier work by the authors*and**their*collabo- rators [P. Cartier*and*D. ... We present*polynomial*time algorithms of two different types. Algorithms of the first type always run*in**polynomial*time*and*succeed almost surely. A. L. Blum*and*J. H. Spencer [J. ...##
###
Page 7575 of Mathematical Reviews Vol. , Issue 98M
[page]

1998
*
Mathematical Reviews
*

From the introduction: “Hall-Litthkewood functions are known to be related to a variety of topics

*in*representation theory, geome- try*and**combinatorics*. ... We present a series of conjectures on these new functions,*and*prove them*in*the two extreme cases: for the shortest possible ribbons (dominoes), OSE Algebraic*combinatorics**and*for sufficiently long ones ...##
###
Recent Developments in Extremal Combinatorics: Ramsey and Turán Type Problems

2011
*
Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)
*

*In*this paper we discuss some recent advances

*in*this subject, focusing on two topics which played an important role

*in*the development of extremal

*combinatorics*: Ramsey

*and*Turán type questions for graphs ... Extremal

*combinatorics*is one of the central branches of discrete mathematics

*and*has experienced an impressive growth during the last few decades. ... Acknowledgments I would like to thank Conlon, Fox, Keevash, Krivelevich

*and*Markman for carefully reading this manuscript

*and*many valuable comments, which greatly improved the presentation. ...

##
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Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width

2014
*
Electronic Journal of Combinatorics
*

mixing for the Tutte

doi:10.37236/4195
fatcat:amjdhchrdzfs3leyuavc3uhgaa
*polynomial*, adjacency-rank ($R_2$-)*polynomial**and*interlace*polynomial*. ...*In*particular Glauber dynamics for the $R_2$-*polynomial*was known to mix rapidly on trees, which led to hope of rapid mixing on a wider class of graphs. ... ,*and**statistics*. ...##
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Page 2283 of Mathematical Reviews Vol. , Issue 83f
[page]

1983
*
Mathematical Reviews
*

*Their*treatment requires some number-theoretic preparation

*in*which regular partitions of Z, are defined

*and*

*their*existence established

*in*many cases.” de Caen, D.; Gregory, D. A.; Pullman, N. J. ... Barlotti, Information theory (French) (Cachan, 1977), pp. 185-187, CNRS, Paris, 1978; see MR 8le:94001],

*and*the study of the packing problem for these sets turns out to be natural

*and*interesting

*in*

*applications*...

##
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Page 2298 of Mathematical Reviews Vol. , Issue 87e
[page]

1987
*
Mathematical Reviews
*

Akiyama

*and*M. Kano.*In*this note it is shown that both complete*bipartite*graphs K(2n—1,2n—1)*and*K(2n, 2n) have star index n +2 (except for some small values of n). H. ... He defines a “separation” prop- erty for*polynomials*(based on the relative locations of*their*zeros)*and*shows that this property is enjoyed by*polynomials*which are formed by linear combinations of the ...
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